Sediment subduction in Hadean revealed by machine learning

Significance The source of Earth’s oldest materials has been debated using traditional approaches to trace elements and isotopes of zircon. Using a single geochemical proxy, like P contents or oxygen isotopes, for source fingerprinting can be ambiguous. Here, we employ machine learning in multidimensional space, incorporating an array of zircon trace elements. This approach is beneficial for low-P zircon, prevalent in the Hadean. We find significant proportions of S-type granite in the Hadean Jack Hills zircon as far back as 4.24 Ga. These proportions exhibit regular variations in supercontinent-like cycles, mirroring patterns observed in global detrital zircon throughout Earth’s history. This suggests that exposed continents, weathering, and subduction-driven plate tectonics were active since the Hadean, facilitating the habitability of early Earth.


Figures S1 to S14
Tables S1 to S4

SI References
Other supporting materials for this manuscript include the following: Datasets 1 to 3

Supporting Information Text
Prudent use of machine learning to recognize S-type zircon Some problems in recent machine learning work.Recently reported machine learning work trying to recognize S-type zircon (1) seems to be problematic upon closer inspection.After reimplementing the machine learning algorithms used in the previous study, we discovered several issues that could impact the accuracy and reliability of the prediction results for Jack Hills (JH) zircon.Firstly, we noticed that there were linearly related features in the model, which violates the assumption of feature independence.Secondly, there appeared to be a possible incorrect use of the data normalization for the prediction set.Specifically, this involves standardizing the feature values based on the mean and standard deviation of prediction set itself, rather than the training set.This could result in the prediction set being classified into three types, even if it only included one type, leading to erroneous predictions and undermining the accuracy of the results.The correct method is to use the training set statistics for data normalization which ensures that the same scaling factors are applied consistently across both the training and prediction sets and thus ensure accurate and reliable results.Additionally, the model showed signs of overfitting, meaning that it performed better on the training set than on the test set.Overfitting is typically caused by a lack of parameter tuning and can significantly affect the ability of the model to make accurate predictions.Taken together, these problems would cause the prediction results for JH zircon to be completely wrong, and thus they must be addressed before any meaningful conclusions can be drawn from the data.Thus, to ensure accurate and reliable results, in our work particular attention has been given to the precise application of techniques including feature selection (Main Text and SI Appendix, Fig. S7), data normalization, and non-overfitting training method (Materials and Methods).
Notably, although our selected 9 elements are independent, Dy and Y still show apparently linearly-correlated relationship, while Lu and Y has modest correlation.To avoid collinearity problems in our experiments, we add an experiment which excludes only Y, turning out F1-score = 0.96 for the test set as well.For this experiment, the fluctuation of S-type proportions for global detrital zircon shows a similar supercontinent-cycle pattern and the same overall trend of the cycles also showing a secular decrease, while the peak of JH S-type zircon becomes slightly lower (Fig. S12).

Our machine learning workflow
Our machine learning workflow went as follows: (i) preprocess original sets to create machinelearning-suitable databases; (ii) train and optimize machine learning models by tuning the hyperparameters of machine learning models to obtain the optimized parameters; (iii) compare the performance of the different machine learning models and select out the best ones that have the highest F1-score; and (iv) predict the types of Jack Hill zircon using the optimized and evaluated machine learning model.

1) Preprocess original datasets to create machine-learning-suitable databases.
Data measurement.Trace element composition of zircon was determined by laser ablationinductively coupled plasma-mass spectrometry (LA-ICP-MS) employing an Element XR HR-ICP-MS instrument (Thermo Fisher Scientific, Bremen, Germany) coupled to a 193 nm ArF excimer laser system (Geolas HD, Lambda Physik, Göttingen, Germany) at the State Key Laboratory of Lithospheric Evolution (SKLLE), Institute of Geology and Geophysics, Chinese Academy of Sciences (IGGCAS).The approach is similar to that outlined in (2) with isotopes measured using a peak-hopping mode with a laser beam diameter of ~32 μm and 5 Hz repetition rate.The laser energy density is ~4.0 J/cm2.The Element XR is equipped with a "jet-interface", which is comprised of a jet sample cone, an X-version skimmer cone, and a high-capacity vacuum pump (On Tool Booster 150, Asslar, Germany).This leads to a signal enhancement in laser sampling mode by a factor of 3-5, resulting in an improved detection capability.Helium is employed as the ablation gas to improve the transporting efficiency of ablated aerosols.NIST SRM 612 reference glass is used for calibration material and GJ-1 and 91500 zircon reference materials are analyzed for data quality control.Silicon (29Si) is used as an internal standard.The resulting data are reduced using the GLITTER program (3).For most trace elements (>0.005 μg/g), the analytical precision (1 RSD) is at ±10%.Data compilation and filtering.As described details in paragraph 7 of the main text, we compiled zircon data including 297,172 trace element data of 14,535 "clean zircon" from the GEOROC database (https://georoc.eu/georoc/new-start.asp).Database 1 (see corresponding statistical table Table S1 for reference, n = 14,535) is designed for calculating the contents and availability of each element in zircon in order to select input features (Fig. 2).Database 2 (see corresponding statistical table Table S3 for reference, n = 1,345) is designed for machine learning, and every zircon in it is a typical non-S-or S-type zircon, or an ancient detrital zircon.All the zircon in Database 2 are further classified into the training set, test set, and prediction set.
2) Train and optimize machine learning models by tuning the hyperparameters of machine learning models to obtain the optimized parameters.
Cross-validation.Cross-validation is a method to determine the prediction performance of a machine learning model (4).By using cross-validation, the raw training set is divided into two new parts: new training set and validation set.The new training set is used to train the machine learning models, while the validation set is specifically used to estimate the prediction error of the machine learning model.In this study, we used the method of Leave-One-Out cross-validation (4) to get validation set, that is, only one sample can be selected from training set into the validation set with the remain samples to train the machine learning model in each iteration.For a dataset of n samples, this training iteration is performed with n times.Then, we could figure out the average prediction error of n validation sets, which is the indicator of prediction potential of machine learning models.
Tuning parameters to select ideal parameters for machine learning model.We applied the grid search method (5) to search for the best hyperparameters for machine learning methods, which is to try every combination of parameters for potential training models.The best-performing parameters, which have the best F1-score on the validation set, is determined by applying the method of cross-validation.After selecting the best parameters of machine learning algorithm, we fed all samples of raw training set into the machine learning model to get the final well-trained model.Finally, the well-trained model with definite parameters is able to be applied to predict unknown detrital zircon.
3) Evaluate model by comparing performance of different machine learning models with accuracy and F1-score.
Model Evaluation.Generally, accuracy and F1-score are most common indicators used to evaluate a machine learning model (6).In our experiment, the S-type zircon is the positive samples and non-S-type is the negative samples.First, we denote the number of correctpredicted S-type zircon as TP, correct-predicted non-S-type zircon as FP, wrong-predicted S-type zircon as FN, wrong-predicted non-S-type zircon as TN.The accuracy is defined by the ratio of all correct-predicted non-S-type zircon and S-type zircon in the test set, calculated by cc TP TN A uracy TP FT TN FN Two indicators Precision and Recall is designed to observe prediction performance of positive samples.Precision represents the probability of correctly-predicted positive samples among the samples predicted to be positive samples, defined as while recall is the probability of being correctly predicted as a positive sample in the original positive samples, calculated by Higher precision and recall rate show that a machine learning method is better.And F1-score is defined as a balanced score of precision and recall, calculated by the following function A good machine learning algorithm usually performs with high precision and high recall, corresponding to high F1-score.Its value is closer to 1 means better performance.
4) Predict the types of Jack Hills zircon using the optimized and evaluated machine learning model.By evaluating and comparing the performance of 11 different machine learning models (details in Materials and Methods) via F1-score and accuracy of low-P S-type zircon we chose the best performed model TSVM.

Caution about the prediction of Hadean zircon based on younger zircon
Lower [Zr] of magma may cause the delayed crystallization of zircon in the Hadean-Archean eons compared to the Phanerozoic (7,8).This likely lead to the caution about the application of our machine learning method recognizing older S-type zircon based on younger zircon.Low [Zr] in early Earth magmas could indeed reduce overall zircon production, aligning with our observed lower abundances (Fig. 4).Yet, our Jack Hills focus is on S-type proportion, not abundance.That is, when S-type zircon and I-type zircon occur at similar crystallization temperatures (9), lower [Zr] is likely to impose a similar effect on the saturation of zircon in I-type and S-type magmas, and as such, zircon saturation in both zircon types is equally delayed and diminished (7).Therefore, this means that under the same low [Zr] conditions of early Earth, the relative proportion of zircon crystallization in both types of magmas may remain unaffected.But this possible limitation of our machine learning method needs to be addressed by some future studies with the same effects on S-type zircon and other types of zircons.
Also, it is impossible to avoid a possible distinction of higher U content in early magma source between Phanerozoic and Hadean-Archean magma sources.To address this concern, we conducted an additional sensitivity test using the raw Th and U contents to train TSVM model and the results illustrate a very similar trend in the proportion of S-type zircon (Fig. S14).This means that a decay-related historical distinction in Th and U contents would not affect our results.

Fig. S1 .
Fig. S1.Simplified geological map of the sample locations of this study and in the literature.

Fig. S2 .
Fig. S2.Distribution and probability density plot by Gaussian Kernel Density Estimation (KDE) of trace element data for Phanerozoic I-and S-type zircon and JH zircon.

Fig. S3 .
Fig. S3.Schematic diagram showing the principle and workflow of the Transductive Support Vector Machine (TSVM) in high-dimensional space.(A) Initial TSVM model using trace element features in the training set.(B) Exchange zircon between support vectors.(C) Update the TSVM model by using trace element features in the training set, as well as weighted trace element features in the test and prediction sets.Dark grey shows the hyperplane that is used to classify Sand non-S-type zircon, light grey shows the hyperplane defined by support vectors.S-, and non-S-type zircos (training set) are shown as red and blue solid circles, respectively.Classified S-and non-S-type zircon (test and prediction sets) are shown as red and blue empty circles.Support vectors (S-and non-S-type zircon) are shown as green and orange circles.The trace element features used in the TSVM model are shown as arrows (not to scale).

Fig. S4 .
Fig. S4.Cluster tree of all zircon (including 1,345 zircon grains) in the data set.This layout allows for a clear visualization of the hierarchical structure of the data set, with closely related samples or clusters appearing closer together (smaller cluster distance) becoming a new cluster.The yaxis cluster distance shows that the distance between different groups or clusters.For instance, if you use a rectangle with cluster distance ranging from 45 to 50 to cut this tree, you will get 3 clusters.The optimal number of clusters will be 2 clusters, which is obtained by the max-height rectangle representing the maximum Euclidean distance between these clusters.

Fig. S5 .
Fig. S5.PCA and t-SNE analysis for the domain of training set, test set, and prediction set.It indicates that the prediction set is located in the domain of training set and test set.

Fig. S6 .
Fig. S6.Learning curve during training of the machine learning algorithm, showing TSVM as an example.

Fig. S8 .
Fig. S8.Sensitivity analysis of the JH zircon proportion regarding different machine learning methods.

Fig. S9 .
Fig. S9.Chondrite-normalized zircon REE compositions of (A-B) modern non-S-and S-type zircon (C-D) non-S-and S-type detrital zircon predicted by the TSVM algorithm.

Fig. S10 .
Fig. S10.Trace element distribution of I-, S-type zircon and detrital zircon.More clear distributions from (B) P-REE+Y 3+ diagram of S-type detrital zircon is shown in (C) P-REE+Y 3+ diagram of Archean S-type detrital zircon (D) P-REE+Y 3+ diagram of Hadean S-type detrital zircon.Two dotted lines indicate the "traditional S-type region" constraining all known S-type zircon and the solid line is the xenotime substitution.The solid symbols are detrital zircon, the red symbols are I-type zircon, the blue symbols are S-type zircon.

Fig. S11 .
Fig. S11.S-type zircon proportion curves of global detrital zircon based on predicted results from two other machine learning algorithms: (A) Logistic Regression (LR) and (B) Multilayer Perceptron (MLP).

Fig
Fig. S12.S-type zircon proportion curves predicted by TSVM using all input features excluding Y.

Fig
Fig. S14.S-type zircon proportions predicted by TSVM using raw Th and U data (i.e., without time decay-related correction) as input features.

Table S1 .
(13,e element composition and availability of zircon showing statistical analysis data based on Dataset 1.The 297,172 trace element data in Dataset 1 used for statistical analysis are compiled from 14,535 "clean zircon"(13,14)from the GEOROC database.It is designed for calculating the contents and availability of each element in zircon in order to select input features.

Table S2 .
Comparison of the performance of 11 machine learning algorithms on the test set.

Table S3 .
S-type zircon proportion of 12 locations with detrital zircon.Hadean Jack Hills zircon